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Trigonometrical Ratios of Standard Angles — Revision Notes

ICSE · Class 9 · Mathematics

Trigonometrical Ratios of Standard Angles revision notes for ICSE Class 9 Mathematics: 4 topics in quick points.

34 questions32 flashcards31 formulas & key relations5 concepts

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A labeled diagram showing an equilateral triangle bisected by an altitude, illustrating how to derive sine, cosine, and tangent for 30° and 60° angles using side lengths 'a' and '2a'.
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Key Topics to Revise

1

1. Trigonometric ratios of 30° and 60°

  • In an equilateral triangle, each angle is 60°.
  • If side BC is 2a and AD is drawn perpendicular to BC, then BD = a.
  • In right triangle ABD, AB = 2a, BD = a, and AD = √3·a.
2

2. Trigonometric ratios of 45°

  • A right-angled isosceles triangle has two equal sides AB = BC = a and one right angle of 90°.
  • The remaining two angles are 45° each.
  • Using Pythagoras theorem, AC = √2·a.
3

3. Standard-angle table and variation from 0° to 90°

  • sin 0° = 0 and cos 0° = 1.
  • sin 90° = 1 and cos 90° = 0.
  • tan 90° is not defined.
4

4. Important identities

  • The Pythagorean identity is sin²A + cos²A = 1 for any angle A.
  • The secant-tangent identity is sec²A - tan²A = 1 for any angle A.
  • The cosecant-cotangent identity is cosec²A - cot²A = 1 for any angle A.

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Full Notes

Key Concepts

In an equilateral triangle with sideIn a rightThe important values are sin 0°As the angle increases from 0°For any angle

Frequently Asked Questions

What are the important topics in Trigonometrical Ratios of Standard Angles for ICSE Class 9 Mathematics?
Key topics in Trigonometrical Ratios of Standard Angles include Trigonometric ratios of 30° and 60°, Trigonometric ratios of 45°, Standard-angle table and variation from 0° to 90°, Important identities. Study these first, then practise questions on each for Class 9 exams.
How should I revise Trigonometrical Ratios of Standard Angles for Class 9 exams?
Learn the core ideas first, then work through the 34 practice questions on Trigonometrical Ratios of Standard Angles. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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